Recent space and airborne observations have noted tenuous cirrus near the tropopause and above deep convective anvil outflow. We use a cloud-resolving model, initialized with aircraft observations taken during the CRYSTAL-FACE experiment, to explore the effects of such cirrus layers on anvil evolution. Numerical simulations demonstrate that anvil cirrus spreads because strong absorption of thermal radiation and emission at cloud base and top creates horizontal heating gradients between the cloud and its environment. The presence of a second layer of cirrus near the tropopause forces the upper part of the anvil to equilibrate to warmer radiative temperatures than would normally be associated with a clear upper atmosphere. Compared to a case without thin cirrus, the associated reduction to heating gradients at anvil cloud top corresponds to reduced anvil spreading and turbulent kinetic energy, by as much as 19% and 40%, respectively. These results suggest that tropopause cirrus can affect climate indirectly, by altering anvil cirrus dynamics.